Question

How do you solve the system of equations `4x+5y=-12` and `5x-5y=-15`?

Answer 1

One method for solving the system of equations is to add the two equations eliminating one of the variables.

Explanation:

There is more than one method for solving the system of equations one method that this system of equation is suited to is adding or subtraction the equations.

One equation has a positive value of 5y the other equation has a negative value of-5y. Adding these equations will cause the y value to disappear.

`4x + 5y = -12`
`+5x -5y = -15` adding these gives
`+9x + 0y = -27`

Now solve for x by dividing by 9

# 9x/9 = -27/9 = x = -3

Now substitute -3 for x in one of equations in order to solve for y

`5(-3) -5y = -15`

`-15 -5y = -15` add -15 to both sides gives

`-15 + 15 -5y = -15 + 15` so

`-5y = 0` dividing both sides by -5 gives

`-5y /-5 = 0/-5 = y = 0`

Answer 2

`x=-3` and `y=0`

Explanation:

Given
[1]`color(white)("XXX")4x+5y=-12`
[2]`color(white)("XXX")5x-5y=-15`

Adding [1] and [2]
[3]`color(white)("XXX")9x=-27`

Dividing [3] by `9`
[4]`color(white)("XXX")x=-3`

Substituting `(-3)` for `x` in [1]
[5]`color(white)("XXX")4 * (-3)+5y=-12`

Simplifying
[6]`color(white)("XXX")5y=0`

Dividing [6] by `5`
[7]`color(white)("XXX")y=0`